At what respective value of a, b, and c would the unit of work, the...

Physics

JAMB 2015

At what respective value of a, b, and c would the unit of work, the joule, be dimensionally similar to M^a L^b T^c?

A. 1, – 2, 1
B. 1, 2, – 2
C. 1, 1, –2
D. 2, 2, 1

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Correct Answer: Option B

Explanation

Work (w) = Force (f) × Distance (d)

Note: f = ma = mass × acceleration

= mass ×acceleration ×distance

= kg ×ms^–2 × m

= kg m2 5^–2

(Note: the dimension of kg = M, M = L & S = T)

Work = ML2 T–2 = Ma Lb Tc

i.e. Ma Lb Tc = as 1, b = 2, c = –2

The value of a, band c = 1, 2, –2

There is an explanation video available below.

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